Could someone explain what direct and inverse variation is?
Also look at attached questions:
imgur[]/Fd03pg0
and
imgur[]/a/opEdofY
Please replace the [] with .com
the [] is equivalent to a: " .com " or .com
Please explain how they are solved. Primarily the 2nd one.
That didn't answer the questions in the images.
since y = ks is the equation for direct variation,
any straight line passing through (0,0) is the graph of a direct variation.
For the 2nd image, since (2,3) is a point on the graph, just draw a line through A and (0,0).
3 = 3/2 * 2, so any point on the line y = 3/2 x will have coordinates where y is 3/2 as big as x. So, as long as x is an even integer, y will also be an integer.
Direct variation and inverse variation are mathematical concepts that describe how two variables are related to each other.
Direct variation is a relationship where two variables change in the same direction. This means that as one variable increases, the other variable also increases, and as one variable decreases, the other variable also decreases. In terms of equations, direct variation can be expressed as y = kx, where y and x are the variables, and k is the constant of variation.
Inverse variation, on the other hand, is a relationship where two variables change in opposite directions. This means that as one variable increases, the other variable decreases, and vice versa. In terms of equations, inverse variation can be expressed as y = k/x, where y and x are the variables, and k is the constant of variation.
Now, let's move on to the attached questions:
First question (imgur[]/Fd03pg0): The question asks to determine whether the relationship between x and y is direct variation, inverse variation, or neither. To solve this, you need to check if the ratio y/x is constant. If the ratio remains the same for different values of x and y, then it is direct or inverse variation.
For example, let's calculate the ratio for the given values:
When x = 2, y = 6 (ratio = 6/2 = 3)
When x = 3, y = 9 (ratio = 9/3 = 3)
When x = 4, y = 12 (ratio = 12/4 = 3)
As you can see, the ratio remains constant (3) for different values of x and y. Therefore, the relationship between x and y is a direct variation.
Second question (imgur[]/a/opEdofY): The question asks to find the inverse variation equation given the values of x and y. To solve this, you need to use the formula of inverse variation, which is y = k/x.
Let's substitute the given values (2, 5) into the equation:
5 = k/2
To isolate k, we can cross-multiply:
5 * 2 = k
k = 10
Now, we have the constant of variation (k = 10). The inverse variation equation is y = 10/x.
By following these steps, you can solve various direct and inverse variation problems.
y = constant * x
is direct
like
y = x is a straight line at 45 degrees to the x axis
y = constant / x
is inverse
like
y = 10/x
if x = 1, y = 10
if x = 2, y = 5
if x = 5, y = 2
if x = 10, y = 1
if x = 100, y = 0.01
NOT a straight line
error fix
if x = 100, y = 0.1